Bigger thigh rises? Lundy strapping? They're freaks?
I'll take the last line next. When I say "frozen in place" I mean that your weight is aligned and distributed in a way that it creates too much friction between the pad and ice and makes it impossible to recover or change direction without first adjusting your body to alleviate that friction and get your skate into a position to engage an edge. The result is a situation where your pad won't slide because of that friction and you can't move because your body isn't aligned/controlled correctly. The only option at that point is to lunge or dive with your stick and body to try and make a save because you don't have the time or ability to use your lower body. This is a terrible situation to be in for a goalie. If you are going to go to the ice, you must do so in a position where you can recover from the ice, even if that means back to standing to move laterally, and that means being able to lift a leg/knee off the ground in the direction you need to go.. You are dropping into positions where you can't lift your leg in order to engage an edge to move - feet behind you, butt down or all your weight on the leading pad, usually the right.
I didn't say one before the other. I said you're only dropping to one, typically your right. Often you do this half butterfly type thing with the trailing leg off the ice. Your weight should be centered towards the push leg, not over the lead leg so you can lift your push one. It's more apparent when you have to move to your right at the same time. Let's look at the very first play of AA vs Black Knights, interestingly a game where you got beat and were disappointed in your (and your team's) performance. You're square to the first guy on a 3-1 with depth where you should be. Your D makes a bad read and essentially turns himself into a cone screening you. The puck goes to your right. And since you have to move that way, you drop all of your weight onto your right knee, with your body way over that leg. You're leading with your head and shoulders into the play rather than the pad. And your left pad trails behind you, off the ice. The result is that the pad sticks to the ice, you lever over the top of it, and you can't even attempt to do anything when the puck goes the other way. Not completely your fault by any means, and you probably couldn't have stopped it anyway. But all you could do was watch. If you would have dropped to both knees when you slid to your right, your weight would have been centered, and you may have been able to engage your right skate or even just throw out your left pad.
But it was a flukey play, so let's look at the next one in that video. You are on your angle with your shoulders square. A shot comes high glove side, with very little angle to the short side. Instead of dropping to both knees in the center of your stance, which would probably have just put the puck into your glove naturally, you drop to your right pad, moving your entire body AWAY from the shot and have to reach all the way out with your glove to make the save. If anything, you should have dropped to your left to bring your body and head behind the puck. But I know dropping left knee only is an issue, so it definitely should have been two knees. If you didn't catch that puck clean because you had to reach out for it, you'd be stuck on your right knee, all the way to the right post with no way to move to your left to stop the rebound from going in. Two plays later, an attacker comes in wide from your left and tries to cut back from behind the net. You think he's going to cut across, so go to slide to your right and lean over that pad, leaving the entire short side exposed. He doesn't score, but it should have been an easy goal. If you drop to both pads, you still would have been square to him and moving across. At 1:35 (pause it right there for a visual representation of what I mean) same thing. You slide, weight on right leg, left leg and arm trailing behind you. Eventually you slide into the play and get your left leg down, but your weight is still over the right. When the play cuts back, you have to lunge to your left to try and cover it, which puts you off balance and teeters you forward. You can't control the rebound, miss the cover, and have to lunge to try to stop the empty net goal. If you would have been centered, you're covering that puck in front of you rather than reaching for it. Do you see what I'm talking about now?
So that's all frustrating and disheartening, I know. But the thing is that you CAN do it right. That's how I know it's a technique thing. What I find most interesting is that you have mentioned playing better in games when you tend to fix the issues more often. Pretty much every save you show in the next video vs Ironside is good. You drop to both knees, square to the puck. And as a result, you can see how much more "quiet" you are. Not moving too much. Pucks are in the chest and gloves easily. Rebounds drop directly in front of you. At the 1:00 mark, you drop evenly and perform a great pivot to the new angle by turning your head->hands->hips and engaging the back edge to push (but get up instead). On the last scramble, you drop evenly so when you dive to cover the puck, everything is in front of you instead of off to the side like in the last game. Your lateral slides are all both knees down, body weight centered. I think you're sliding further and easier as a result. At 1:30 you make a great save moving from your right to left with good technique. At 1:43 you make a good save and are able to regain your edges because you're balanced. You end up diving for the puck but I think that was more because you lost sight of it and were on the wrong foot when you realized where it was. You probably would have been able to push with your right foot if you had seen it the whole way. 2:41 is another good lateral push to the new angle. Even the last goal was good technique. You were on both knees and were able to adjust to try and make the save. Just a bad bounce to an uncovered guy. But the attempt wasn't a desperation one where you just threw something out there with no chance.
Hopefully that all helps.